al-Salamu `Aleykum,
Since I've been going through the books of history, as you know they're full of stories, some have truth to them and some are fabrications, usually chainless narratives having no sources.
So since we've had to post such horrible things, we might as well post some authentic reliable material to remind the readers of the truth... There definitely are quite a bunch of narrations which show the good relationship they had, I picked this one.
Al-Bayhaqi has made Takhreej of this in his "al-I`tiqad":
أَخْبَرَنَا أَبُو طَاهِرٍ الْفَقِيهُ، أنا أَبُو بَكْرٍ مُحَمَّدُ بْنُ الْحُسَيْنِ الْقَطَّانُ، ثنا أَحْمَدُ بْنُ يُوسُفَ السُّلَمِيُّ، ثنا مُحَمَّدُ بْنُ يُوسُفَ، قَالَ: ذَكَرَ سُفْيَانُ، عَنْ جَعْفَرِ بْنِ مُحَمَّدٍ، عَنْ أَبِيهِ، قَالَ: قَالَ عَلِيٌّ: إِنِّي لأَرْجُو أَنْ أَكونَ، وَطَلْحَةُ، وَالزُّبَيْرُ مِنَ الَّذِينَ قَالَ اللَّهُ : وَنَزَعْنَا مَا فِي صُدُورِهِمْ مِنْ غِلٍّ إِخْوَانًا عَلَى سُرُرٍ مُتَقَابِلِينَ. وَكَانَ أَمِيرُ الْمُؤْمِنِينَ رَضِيَ اللَّهُ عَنْهُ، بَرِيئًا مِنْ قَتْلِ عُثْمَانَ، يَقُولُ: وَاللَّهِ مَا قَتَلْتُ وَلا أَمَرْتُ وَلا رَضِيتُ وَلا شَارَكْتُ فِي قَتْلِ عُثْمَانَ، وَلَكِنْ غُلِبْتُ، وَكَانَ يَقُولُ: إِنِّي لأَرْجُو أَنْ أَكُونَ أَنَا، وَعُثْمَانُ مِنَ الَّذِينَ قَالَ اللَّهُ : وَنَزَعْنَا مَا فِي صُدُورِهِمْ مِنْ غِلٍّ إِخْوَانًا عَلَى سُرُرٍ مُتَقَابِلِينَ
[Al-Baqir said: `Ali ibn abi Talib said: "I wish that I and Talhah and al-Zubayr would be from those whom Allah described: {And We will remove whatever is in their breasts of resentment, [so they will be] brothers, on thrones facing each other (In paradise)}" and Ameer-ul-Mu'mineen may Allah be pleased with him was innocent from the murder of `Uthman, he would say: "By Allah I never took part in the killing nor did I order it nor am I pleased with it and I never participated in `Uthman's murder, but I failed (to help because of the rebels)." And he used to say: "I wish that I and `Uthman would be as Allah described: {Brothers on thrones facing each other}."]
We begin with the Rijal, starting with Muhammad bin Muhammad abu Tahir al-Faqih al-Shafi`i, he is Imam al-Muhadditheen in Naysabur according to al-Subki in his Tabaqat, next is Abu Bakr Muhammad bin al-Husayn bin al-Hasan al-Naysaburi and al-Dhahabi said "Sama`uhu Sahih" in al-Siyar, next is Ahmad bin Yusuf bin Khalid al-Sulami a big Thiqah, next is Muhammad bin Yusuf al-Firyabi the popular Thiqah who narrates from Sufiyan al-Thawri "Ameer-ul-Mu'mineen fil-Hadith", he narrates from Ja`far bin Muhammad from his father Muhammad bin `Ali from their father `Ali ibn abi Talib the above Hadith.
This Hadith is narrated from `Ali with quite a few chains, such as that of Tafsir al-Tabari:
حَدَّثَنَا الْحَسَنُ، قَالَ: ثنا يَزِيدُ بْنُ هَارُونَ، قَالَ: أَخْبَرَنَا هِشَامٌ، عَنْ مُحَمَّدٍ، قَالَ: اسْتَأْذَنَ الأَشْتَرُ عَلَى عَلِيٍّ
and
حَدَّثَنَا الْحَسَنُ، قَالَ: ثنا إِسْحَاقُ الأَزْرَقُ، قَالَ: أَخْبَرَنَا عَوْفٌ، عَنِ ابْنِ سِيرِينَ، بِنَحْوِهِ
and
حَدَّثَنَا الْحَسَنُ، قَالَ: ثنا يَعْقُوبُ بْنُ إِسْحَاقَ الْحَضْرَمِيُّ، قَالَ: ثنا السَّكَنُ بْنُ الْمُغِيرَةِ، قَالَ: ثنا مُعَاوِيَةُ بْنُ رَاشِدٍ، قَالَ: قَالَ عَلِيٌّ
Or Tafsir `Abdul-Razzaq al-San`ani:
عَنْ مَعْمَرٍ، عَنْ قَتَادَةَ، فِي قَوْلِهِ تَعَالَى:وَنَزَعْنَا مَا فِي صُدُورِهِمْ مِنْ غِلٍّ، قَالَ: قَالَ عَلِيُّ بْنُ أَبِي طَالِبٍ
Or Fada'il al-Sahabah li-Ahmad:
حَدَّثَنَا جَعْفَرُ بْنُ مُحَمَّدٍ، قَالَ: نا عُبَيْدُ اللَّهِ بْنُ مُعَاذٍ، نا أَبِي، نا الأَشْعَثُ، عَنْ مُحَمَّدِ بْنِ سِيرِينَ، عَنْ أَبِي صَالِحٍ، عَنْ عَلِيٍّ
And a couple of others...